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Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators

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Abstract

In this paper, we consider optimization problems with equilibrium constraints. We study the Wolfe-type dual problem for the optimization problems with equilibrium constraints under the convexity assumptions using convexificators. A Mond–Weir-type dual problem is also formulated and studied for the optimization problems with equilibrium constraints under convexity and generalized convexity assumptions using convexificators. Weak duality theorems are established to relate the optimization problems with equilibrium constraints and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification.

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Acknowledgments

The authors are grateful to anonymous referees for careful reading of the manuscript, which improved the paper in its present form. The first author is supported by the Council of Scientific and Industrial Research, New Delhi, India, through Grant No: 09/013(0388)/2011-Emr.

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  1. Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    Yogendra Pandey & Shashi Kant Mishra

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  1. Yogendra Pandey
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  2. Shashi Kant Mishra
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Correspondence to Yogendra Pandey.

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Pandey, Y., Mishra, S.K. Duality for Nonsmooth Optimization Problems with Equilibrium Constraints, Using Convexificators. J Optim Theory Appl 171, 694–707 (2016). https://doi.org/10.1007/s10957-016-0885-2

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  • DOI: https://doi.org/10.1007/s10957-016-0885-2

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